The facility location problem with Bernoulli demands

This paper presents the facility location problem with Bernoulli demands. In this capacitated discrete location stochastic problem the goal is to define an a priori solution for the locations of the facilities and for the allocation of customers to the operating facilities that minimizes the sum of the fixed costs of the open facilities plus the expected value of the recourse function. The problem is formulated as a two-stage stochastic program and two different recourse actions are considered. For each of them, a closed form is presented for the recourse function and a deterministic equivalent formulation is obtained for the case in which the probability of demand is the same for all customers. Numerical results from computational experiments are presented and analyzed.     

OPTIMAL PROJECT SEQUENCING WITH RECOURSE AT A SCARCE RESOURCE

We develop a dynamic prioritization policy to optimally allocate a scarce resource among K projects, only one of which can be worked on at a time. When the projects' delay costs differ, the problem (a “restless bandit”) has not been solved in general. We consider the policy of working on the project with the highest expected delay loss as if the other project was completely finished first (although recourse is allowed). This policy is optimal if: (1) the delay cost increases with the delay regardless of the performance state, (2) costs are not discounted (or, discounting is dominated by delay costs), (3) projects are not abandoned based on their performance state during processing at the scarce resource, and (4) there are no stochastic delays. These assumptions are often fulfilled for processing at specialized resources, such as tests or one‐off analyses.     

Two-stage stochastic mixed-integer linear programming: The conditional scenario approach

In this paper we consider the two-stage stochastic mixed-integer linear programming problem with recourse, which we call the RP problem. A common way to approximate the RP problem, which is usually formulated in terms of scenarios, is to formulate the so-called Expected Value (EV) problem, which only considers the expectation of the random parameters of the RP problem. In this paper we introduce the Conditional Scenario (CS) problem which represents a midpoint between the RP and the EV problems regarding computational tractability and ability to deal with uncertainty. In the theoretical section we have analyzed some useful bounds related to the RP, EV and CS problems. In the numerical example here presented, the CS problem has outperformed both the EV problem in terms of solution quality, and the RP problem with the same number of scenarios as in the CS problem, in terms of solution time.     

Profitability of loyalty reward programs: An analytical investigation

Loyalty programs, as a prevalent CRM strategy, aim to enhance customers’ loyalty and thereby increase a firm’s long-term profitability. Recent analytical and empirical studies demonstrate inconsistent findings on the efficacy of loyalty programs in fulfilling these goals. In this study, an analytical model is developed to analyze the effect of customers’ valuation and their post-purchase satisfaction level on a loyalty program’s profitability. The results reveal how customers’ satisfaction plays a significant role in profitability of loyalty programs. We consider a profit-maximizing firm selling a good or service through two periods. Valuation is modeled as a deterministic parameter, as well as a stochastic variable with two arbitrary distributions. Depending on the customers’ valuation distribution, the model results in either a linear or a nonlinear optimization problem. Optimization problems are solved analytically, in terms of the model parameters. The obtained solutions provide some useful insights into the effects of customers’ satisfaction on the profitability of loyalty programs. Specifically, it is shown that depending on the customers’ satisfaction level, it may be optimal not to offer a loyalty reward.     

多车型确定性动态车辆调配问题

详细地描述了多车型确定性动态车辆调配问题.建立了问题的线性规划模型,鉴于线性模型的缺点,构造一个线性函数来近似目标函数中未来时段部分,从而建立起问题的时空分解模型,把问题从时间和空间上分解为多个单时段单节点问题,并根据单时段单节点问题的特点设计简单的排序求解方法.最后给出了问题的完整求解过程,从而使问题能够得到有效解决.     

具有灰色随机动态特征的供应链牛鞭效应的鲁棒性分析

供应链的随机动态性和牛鞭效应加大了供应链系统建模鲁棒性的难度,供应链的平稳运行是供应链管理的重要基础。针对具有区间灰色特征的随机动态供应链系统,以线性时不变系统作为研究基础,提出使用Markov算法解决供应链系统随机线性跳变的鲁棒性问题,获取了判定随机动态供应链系统鲁棒性的一个有效度量指标。算例结果表明:随机动态供应链系统的牛鞭放大效应与节点间的变化幅度和长期概率的平均值均无关;Markovian跳变线性供应链系统的整体性能不能仅凭单个节点的性能来预测;供应链运作的不确定性将会导致系统整体性能的降低。     

Why good practice of OR is not enough—Ethical challenges for the OR practitioner

This paper develops the idea that following rules of good OR practice is necessary, but not sufficient for ethical OR. Several challenges of introducing ethical aspects into OR are discussed, evidencing difficulties and ambiguities in the relationship to be established between the OR practitioner and his/her clients, decision-makers or stakeholders. It shows that neither analysis nor modelling work nor the choice of analytical tools is entirely ethically neutral; incomparability, incommensurability and incertitude must be dealt with. The purpose of this article is to detail several difficulties or dilemmas an OR practitioner may be confronted with in the course of his or her assignment. In such situations, following rules of good practice may not be sufficient to indicate how to act in a morally good way. This paper aims at stimulating reflection by structuring the debate; it may leave the reader unsettled—unsettlement being a result and even aim of many discussions in moral philosophy.     

Zero Expected Wealth Taxes: A Mirrlees Approach to Dynamic Optimal Taxation

In this paper, I consider a dynamic economy in which a government needs to finance a stochastic process of purchases. The agents in the economy are privately informed about their skills, which evolve stochastically over time; I impose no restriction on the stochastic evolution of skills. I construct a tax system that implements a symmetric constrained Pareto optimal allocation. The tax system is constrained to be linear in an agent's wealth, but can be arbitrarily nonlinear in his current and past labor incomes. I find that wealth taxes in a given period depend on the individual's labor income in that period and previous ones. However, in any period, the expectation of an agent's wealth tax rate in the following period is zero. As well, the government never collects any net revenue from wealth taxes.     

PORTFOLIO MODELING IN MULTIPLE-CRITERIA SITUATIONS UNDER UNCERTAINTY

There have been many models for portfolio selection, but most do not explicitly include uncertainty and multiple objectives. This paper presents an approach that includes these aspects using a form of stochastic integer programming with recourse. The method involves the use of a time-based decision tree structure called a “project tree.” Using this basic format, an illustrative six-project example is presented and analyzed. Various forms of objectives are discussed, ranging from the maximization of expected portfolio value to the maximization of the minimum weighted portfolio deviation from two goals. In each case, formulated numerical problems are given, and the solutions derived are presented. The approach is shown to be very flexible and capable of handling a variety of situations and objectives.     

STOCHASTIC COST-VOLUME-PROFIT ANALYSIS WITH A LINEAR DEMAND FUNCTION

In this paper we incorporate a linear demand function to model the price-volume causal relationship into stochastic cost-volume-profit (CVP) analysis. We assume that the objective function is to maximize expected profit; other objective functions are also discussed and compared. A linear stochastic model follows from which probabilistic statements can be easily obtained if the random variables are assumed to be multivariate normal. The basic framework is shown to be a special case of project value maximization where project value is the cash flow of the project discounted for time and risk according to the capital asset pricing model. Moreover, an intertemporal extension that considers inventory is developed. In summary, a new approach to stochastic CVP analysis that incorporates the management decision process in an uncertain environment is developed.     

Integrality in Stochastic Inventory Models

We study several finite‐horizon, discrete‐time, dynamic, stochastic inventory control models with integer demands: the newsvendor model, its multi‐period extension, and a single‐product, multi‐echelon assembly model. Equivalent linear programs are formulated for the corresponding stochastic dynamic programs, and integrality results are derived based on the total unimodularity of the constraint matrices. Specifically, for all these models, starting with integer inventory levels, we show that there exist optimal policies that are integral. For the most general single‐product, multi‐echelon assembly system model, integrality results are also derived for a practical alternative to stochastic dynamic programming, namely, rolling‐horizon optimization by a similar argument. We also present a different approach to prove integrality results for stochastic inventory models. This new approach is based on a generalization we propose for the one‐dimensional notion of piecewise linearity with integer breakpoints to higher dimensions. The usefulness of this new approach is illustrated by establishing the integrality of both the dynamic programming and rolling‐horizon optimization models of a two‐product capacitated stochastic inventory control system.     

Bridging Practice and Theory: A Design Science Approach

Despite ambitious efforts in various fields of research over multiple decades, the goal of making academic research relevant to the practitioner remains elusive: theoretical and academic research interests do not seem to coincide with the interests of managerial practice. This challenge is more fundamental than knowledge transfer, it is one of diverging knowledge interests and means of knowledge production. In this article, we look at this fundamental challenge through the lens of design science, which is an approach aimed primarily at discovery and problem solving as opposed to accumulation of theoretical knowledge. We explore in particular the ways in which problem‐solving research and theory‐oriented academic research can complement one another. In operations management (OM) research, recognizing and building on this complementarity is especially crucial, because problem‐solving–oriented research produces the very artifacts (e.g., technologies) that empirical OM research subsequently evaluates in an attempt to build explanatory theory. It is indeed the practitioner—not the academic scientist—who engages in basic research in OM. This idiosyncrasy prompts the question: how can we enhance the cross‐fertilization between academic research and research practice to make novel theoretical insights and practical relevance complementary? This article proposes a design science approach to bridge practice to theory rather than theory to practice.     

Sequencing and Scheduling Appointments with Potential Call‐In Patients

This paper studies appointment scheduling for a combination of routine patients who book well in advance and last‐minute patients who call for an appointment later that same day. We determine when these same‐day patients should be scheduled throughout the day, and how the prospect of their arrivals affects the appointment times of the routine patients. By formulating the problem as a stochastic linear program, we are able to incorporate random and heterogeneous service times and no‐show rates, ancillary physician tasks, and appointment delay costs for same‐day patients who prefer to see the doctor as early as possible. We find that the optimal patient sequence is quite sensitive to the no‐show probabilities and the expected number of same‐day patients. We also develop two simple heuristic solutions to this combinatorial sequencing problem.     

Portfolio Selection Using Stochastic Dominance Criteria

The direct application of stochastic dominance criteria to portfolio selection problems has been thought impractical because an extremely large number of combinations of returns must be considered. This paper proposes and evaluates a rigorous statistical procedure for sampling the combinations of returns on candidate risky assets so that stochastic dominance criteria may be used directly in an efficient linear programming model for portfolio selection. The sampling scheme exploits the association of the return on each candidate stock with the return on a market index in a manner analogous to the Sharpe single-index model, thereby eliminating the large number of combinations with probabilities close to or equalling zero. Portfolios computed by the proposed linear programming stochastic dominance model are compared with those computed by the single-index quadratic programming model, using 180 months of recent data on a sample of NYSE common stocks.     

Probabilistic dominance criteria for comparing uncertain alternatives: A tutorial

This paper is a tutorial which demonstrates the current state-of-the-art methods for incorporating risk into project selection decision making. The projects under consideration might be R&D, IT, or other capital expenditure programs. We will show six decision making methods: 1. mean-variance (MV), 2. mean-semivariance, 3. mean-critical probability, 4. stochastic dominance, 5. almost stochastic dominance (ASD), and 6. mean-Gini. We will also describe the assumptions about the risk attitudes of the decision maker which are associated with each of the techniques. While all these methods have been previously applied elsewhere, this is the first paper which shows all of their applications in the project selection context, together with their interrelationships, strengths and weaknesses. We have applied all six techniques to the same group of five hypothetical projects and evaluated the resulting nondominated sets. Among the methods reviewed here, stochastic dominance is recommended because it requires the least restrictive assumptions. ASD and mean-Gini are recommended when stochastic dominance is not practical or when it does not yield definitive choices. MV, mean-semivariance, and mean-critical probability are shown to be flawed.     

Enhancing the Practical Relevance of Research

This article seeks to encourage scholars to conduct research that is more relevant to the decisions faced by managers and policymakers, and addresses why research relevance matters, what relevance means in terms of a journal article, and how scholars can increase the relevance of their research. I define relevant research papers as those whose research questions address problems found (or potentially found) in practice and whose hypotheses connect independent variables within the control of practitioners to outcomes they care about using logic they view as feasible. I provide several suggestions for how scholars can enhance research relevance, including engaging practitioners in on‐campus encounters, at managerial conferences, and at crossover workshops; conducting site visits and practitioner interviews; working as a practitioner; and developing a practitioner advisory team. I describe several ways that scholars can convey relevant research insights into practitioners, including presenting at practitioner conferences, writing for practitioners in traditional crossover journals and in shorter pieces like op‐eds and blogs, and attracting the interest of those who write columns, blogs, and articles about research for practitioners. I conclude by describing a few ways that academic institutions can encourage more relevant research, focusing on journals, professional societies, and doctoral programs.     

A note on the facility location problem with stochastic demands

In this research note that the single source capacitated facility location problem with general stochastic identically distributed demands is studied. The demands considered are independent and identically distributed random variables with arbitrary distribution. The unified a priori solution for the locations of facilities and for the allocation of customers to the operating facilities is found. This solution minimizes the objective function which is the sum of the fixed costs and the value of one of two different recourse functions. For each case the recourse function is given in closed form and a deterministic equivalent formulation of the model is presented. Some numerical examples are also given.     

基于CVaR约束的多产品订货风险决策模型

过去随机环境下多产品订货往往以期望值作为唯一决策准则,没有将风险控制纳入决策范畴,与实际决策过程不相符合.为给具有不同风险偏好的决策者提供合适的决策分析工具,文章在分析投资组合和产品组合存在某种相似性的基础上,借鉴金融工程领域广泛应用的条件风险值方法,建立多产品最优订货决策模型,并对模型进行了检验,发现它完全符合决策者的直觉要求.而且,由于所建的模型最终可以表示为一个线性规划问题,因此即使是大规模的产品组合问题也可以借助工具软件求解.     

A two-stage stochastic programming approach to employee scheduling in retail outlets with uncertain demand

This paper describes an employee scheduling system for retail outlets; it is a constraint-based system that exploits forecasts and stochastic techniques to generate schedules meeting the demand for sales personnel. Uncertain scenarios due to fluctuating demand are taken into account to develop a stochastic operational optimization of staffing levels. Mathematically, the problem is stated as a mixed-integer linear programming problem. Simulations with store data belonging to a major Swiss retailer show the effective performance of the proposed approach. The schedule quality is assessed through comparison with a deterministic scheduling package, which has been used at several outlets in Switzerland.